The first one is the value of the function if the inverse function is the input.

So if f(x) = x + 1, f^-1(x) = x - 1; then f[f^-1(x)] = (x - 1) + 1 = x

The second one is the value of the inverse function if the original function is the input.

So if f(x) = x + 1, f^-1(x) = x - 1, then f^-1[f(x)] = (x + 1) - 1 = x

f(f–1(x)) = x = f–1(f(x))

function & inverse function cancel themselves out.

Ex: 10^ and log cancel themselves out.

f(f-1(x)) = 1/f-1 (f(x))

vlue of x and inverse function of x